Find the average value of the function

Question

find the average value of the function f(t)=-5te^{-t^2} on the interval [0,5]

Answer 1

The average value is the integral of the function from 0 to 5 divided by 5.

 

The antiderivative of  the function is   -(5/2) e^{-t^2}  

 

So the average is  (5/2) [1 - e^-25 ]/5

Since e^-25 is a very small number, a good approximate value is 1/2